I think the biggest difference would be the regulations that you have to follow and know in different countries. The plan.do.check.act cycle, PM processes, and design controls can be applied to any situation. The biggest hurdle would be anything to do with culture such as enterprise environmental factors. Being in a different culture would mean dealing with a different work ethic and way of communicating. Something as standard as holding a kickoff meeting might be challenging. In some cultures, authority is not challenged and they expect to be told what to do as opposed to being part of a conversation. They might feel like they are doing your job for you as the project manager.

Managing a project between various countries would be challenging but achievable. I think responsibilities of each country would have to be clearly defined. I also believe it helps for each team in the various countries to be as diverse as possible because it helps others to understand another culture. For example, in the US its good to have diversity because someone on that team might know or have a better understanding of a country you are working with. Having someone close to you who works with you everyday explain and help you get use to that other country is a life saver.